AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES

Title & Authors
AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES
Park Jong-Jin; Zhang Yong;

Abstract
We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeomorphism f has more than two fixed points on $\small{S^1}$, then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in [6] is not true.
Keywords
average shadowing property;$\small{{\delta}}$-average-pseudo-orbit;shadowing property(pseudo orbit tracing property);$\small{{\delta}}$-pseudo-orbit;chain recurrent;
Language
English
Cited by
1.
SOME PROPERTIES OF THE STRONG CHAIN RECURRENT SET,;;;

대한수학회논문집, 2010. vol.25. 1, pp.97-104
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